Sobolev and BV functions on RCD spaces via the short-time behaviour of the heat kernel

2022/12/07 by Camillo Brena, Brena, Camillo, Enrico Pasqualetto +3
Mathematics · #26A45 #35K08 #46E35 #49J52 #53C23 #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.03910

openalex publication_date 2022/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the setting of finite-dimensional RCD(K,N) spaces, we characterize the p-Sobolev spaces for p∈(1,∞) and the space of functions of bounded variation in terms of the short-time behaviour of the heat flow. Moreover, we prove that Cheeger p-energies and total variations can be computed as limits of nonlocal functionals involving the heat kernel.

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